Chilean Kindergarten Children’s Beliefs About Mathematics:Family Matters

M. Francisca del RíoUniversidad Diego Portales de Chile

Katherine StrasserPontificia Universidad Católica de Chile

Dario CvencekUniversity of Washington

María Inés SusperreguyPontificia Universidad Católica de Chile

Andrew N. MeltzoffUniversity of Washington

This study examines the relations among parental beliefs and practices about mathematics, children’sbeliefs about mathematics, participants’ gender, and family socioeconomic status (SES). The study wasconducted in Chile, a country with significant gender gaps in standardized test results in mathematics,with boys receiving significantly higher scores than girls. One hundred eighty Chilean kindergarteners(Mage � 5.6 years) of low and high SES completed both implicit and explicit measures of their beliefsabout mathematics. Children’s mothers and fathers also completed adult versions of these tests, as wellas measures of home numeracy practices. This combination of child and parental assessments (bothmother and father), including both implicit and explicit measures, provided a wider range of measuresthan in previous studies. On implicit measures of math–gender stereotypes, boys showed the math � boystereotype significantly more strongly than girls did. Both fathers and mothers showed this stereotype onboth implicit and explicit measures. Fathers also linked me � math (math self-concept) more stronglythan mothers on both implicit and explicit measures. Kindergarten girls’ implicit math self-concept wasexplained by a combination of parents’ math self-concepts and SES. Taken together, these results showthat by 5 years of age children are already developing beliefs about “who does math” in their culture, andthat parental beliefs and practices are significantly linked to children’s stereotypes and self-conceptsabout mathematics before they enter formal schooling.

Keywords: math–gender stereotypes, math self-concepts, parental beliefs, SES, identity development

Supplemental materials: http://dx.doi.org/10.1037/dev0000658.supp

Early mathematical skills are critical for later career success inscience, technology, engineering, and mathematics (STEM; Den-ton & West, 2002; Geary, 2011; Gunderson, Ramirez, Levine, &Beilock, 2012; Uttal, Miller, & Newcombe, 2013). Building early

and positive beliefs about mathematics can have cascading effectsfor STEM skill development (Newcombe et al., 2009; Watts,Duncan, Siegler, & Davis-Kean, 2014). In addition, gender stereo-types about mathematics may contribute to gender differences inattitudes, participation, and performance in STEM fields (Smed-ing, 2012; Steffens, Jelenec, & Noack, 2010).

Do children come to school with beliefs and stereotypes about“who does mathematics?” To address this developmental question,one needs to examine children’s beliefs about mathematics andtheir relations to family factors before first grade. This currentstudy investigated stereotypes in Chilean children, and how moth-ers’ and fathers’ beliefs about mathematics, as well as parentalinvolvement in mathematics-related activities, contribute to chil-dren’s beliefs about mathematics by 5 years of age, before theystart formal schooling.

The Value of Studying Children in Chile

Studying early beliefs about mathematics in young childrenfrom Chile is important for three reasons. First, Chile has one ofthe largest gender gaps in the international PISA mathematics

M. Francisca del Río, School of Education, Universidad Diego Portalesde Chile; Katherine Strasser, School of Psychology, Pontificia UniversidadCatólica de Chile; Dario Cvencek, Institute for Learning & Brain Sciences,University of Washington; María Inés Susperreguy, School of Education,Pontificia Universidad Católica de Chile; Andrew N. Meltzoff, Institute forLearning & Brain Sciences, University of Washington.

Support for this research was provided by the grants from the ChileanNational Fund of Scientific and Technology Development (Fondecyt N°1150156) and the U.S. National Science Foundation (SBE-1640889; HRD1661285). Thanks to participating principals, teachers, mothers, fathers,and students, and to our research assistants for their valuable work.

Correspondence concerning this article should be addressed to M.Francisca del Río, School of Education, Universidad Diego Portales deChile, Vergara 210, Santiago, Chile. E-mail: francisca.delrio@mail.udp.cl

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Developmental Psychology© 2018 American Psychological Association 2018, Vol. 1, No. 999, 0000012-1649/18/$12.00 http://dx.doi.org/10.1037/dev0000658

1

assessment. Among the 72 countries who participate in this inter-national testing, the gender gap in mathematics (with boys scoringhigher than girls) is greater than 20 points in only six countries,one of which is Chile (Organisation for Economic Co-operationand Development [OECD], 2015). This pattern is also observed inthe Chilean standardized national school achievement test, taken ineighth and tenth grade, where this gender gap in mathematicsachievement is twice as large for low socioeconomic status (SES)students compared to high SES students (Measurement System ofEducation Quality [SIMCE], 2013). Career choice and access tothe better-paid jobs are also not equally distributed by gender inChile. In 2012, 50% of Chilean parents reported that they expectedtheir sons to work in STEM fields versus only 20% with suchexpectations about their daughters (OECD, 2015; see also Stoet,Bailey, Moore, & Geary, 2016). A gap of this magnitude was onlypresent in two other OECD countries. In fact, in the last 25 years,fewer than 20% of undergraduate STEM students in Chile werewomen (Blázquez, Álvarez, Bronfman, & Espinosa, 2009).

Second, a recent debate across the social sciences has questionedthe generalizability of research findings obtained from Western, Ed-ucated, Industrialized, Rich, and Democratic (WEIRD) cultures (Hen-rich, Heine, & Norenzayan, 2010). The oversampling of NorthAmerican participants, in particular, might skew our understandingof child development and family interactions. The current workexamines understudied child populations in Chile and appliescognitive-developmental science to a non-WEIRD sample. To ourknowledge, no previous studies have tested beliefs about mathe-matics in parents and their young children from developing coun-tries (Chile qualifies as a developing country; United Nations,2016).

Third, there is a growing Latino student culture in the UnitedStates. Latinos are the fastest growing ethnic group in the UnitedStates, and about 25% of all public school children are Latino(Lopez & Velasco, 2011). Given the continuing increase of immi-grants from Latin America, it is important for U.S. educators anddevelopmental psychologists to understand how the parental sys-tems function in Latino cultures, and how parental beliefs andpractices about mathematics may be related to young children’sown developing beliefs about mathematics (Rivas-Drake &Marchand, 2016).

Preschool Children’s Beliefs About Mathematics

Young children’s interest in mathematics and other STEM fieldsis linked both to academic (e.g., skills and facts) and nonacademic(beliefs and attitudinal) factors. We focus on two types of nonac-ademic beliefs that are linked to children’s early interest in math-ematics. The first is children’s belief about whether boys or girlsare more likely to participate in mathematical activities. If thistakes a societally characteristic form, it can be called a math–gender stereotype, the stereotype that math � male. Previousresearch suggests that gender gaps in mathematics are driven atleast in part by pervasive cultural stereotypes about who doesmathematics (e.g., Cvencek, Kapur, & Meltzoff, 2015; Kurtz-Costes, Rowley, Harris-Britt, & Woods, 2008). The second is amath self-concept—that is how strongly the child links me andmath (“I consider myself to be a math person”).

The available studies (mostly in WEIRD samples) suggest thatboys and girls do not differ in their math self-concepts at the very

youngest ages tested so far (Marsh, Ellis, & Craven, 2002), how-ever it is also reported that by late elementary school, girls beginto rate their mathematical ability lower than boys do, even thoughgirls do not rate their ability lower than boys do in other domains(Cvencek, Meltzoff, & Greenwald, 2011; Herbert & Stipek, 2005).Children’s stereotypes and self-concepts about mathematics taptwo differentiable beliefs that children may hold, and they caninteract in interesting ways. Stereotypes refer to beliefs about ageneralized social group to which one may or may not belong(“math � boys”), whereas self-concepts refer to the self (“me �math”). For example, gender-related stereotypes about academicability and “brilliance” are acquired early and have an effect onchildren’s stated interests (Bian, Leslie, & Cimpian, 2017). Suchstereotypes have been implicated in undermining young girls’mathematical performance, their forming identification with thisacademic subject, and their aspirations about the future (Coyle &Liben, 2016; Master, Cheryan, & Meltzoff, 2017). Although re-search shows that young elementary schoolchildren in K–2ndgrades hold some math–gender stereotypes (e.g., Ambady, Shih,Kim, & Pittinsky, 2001; Cvencek et al., 2011; Galdi, Cadinu, &Tomasetto, 2014; Heyman & Legare, 2004; Steele, 2003), to ourknowledge, only one previous study has examined the age ofacquisition of math–gender stereotypes by extending downward toinclude a preschool sample (del Río & Strasser, 2013). No previ-ous research has systematically examined whether and how kin-dergarten children’s gender stereotypes about mathematics may berelated to children’s emerging math self-concept and how thesebeliefs relate to the beliefs and practices of the children’s ownparents.

Turning now to math self-concepts, the classic developmentalresearch in this area has focused on elementary and secondaryschool students (Eccles, Wigfield, Harold, & Blumenfeld, 1993;Wigfield et al., 1997), with less attention given to the mathself-concepts before children enter formal schooling.

Implicit and Explicit Beliefs About Mathematics

Human behavior is not only guided by conscious (explicit andcontrolled) processes, but also by more unconscious (implicit andautomatic) processes (Gawronski & Payne, 2010). Traditionally,explicit measures have been used to investigate stereotypes andprejudice in children. However, prior studies have also highlightedthe challenges of asking children as young as kindergarten tointrospect and verbally report about themselves and their socialgroups as required by most explicit measures (Killen, McGlothlin,& Henning, 2008; Olson & Dunham, 2010). Recent researchsuggests that implicit measures may provide a useful tool forbypassing these linguistic and introspective challenges. Critically,the empirical results demonstrate that implicit math–gender ste-reotypes and implicit math self-concepts are significant predictorsof children’s actual mathematics achievement—accounting foradditional variance over and above the explicit measures (e.g.,Cvencek et al., 2015; Steffens et al., 2010).

Development of Implicit and Explicit BeliefsAbout Math

To date, only a few studies have assessed both implicit andexplicit math–gender stereotypes in the same children. Research

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2 DEL RÍO ET AL.

using a child-friendly adaptation of the Implicit Association Test(IAT) with U.S. elementary schoolchildren documented implicitmath–gender stereotypes as early as 1st–2nd grade (Cvencek et al.,2011). Galdi et al. (2014) also found evidence of implicit math–gender stereotypes at age 6 among Italian girls (but not boys) andthat implicit stereotypes were not consistent with children’s ex-plicit stereotypes (see also Tomasetto, Galdi, & Cadinu, 2012).Other work also suggests that implicit stereotypes may emergebefore explicit ones in children (Ambady et al., 2001; Steele,2003).

Work with U.S. and Singaporean 1st–5th grade boys and girls,found that stronger math–gender stereotypes (i.e., the belief thatboys � math) are associated with stronger math self-concepts forboys and weaker math self-concepts for girls (Cvencek et al.,2011; Cvencek, Meltzoff, & Kapur, 2014). In addition, thesestudies found that math self-concepts are weaker and less stablethan math–gender stereotypes.

Taken together, these results suggest that (a) math stereotypesmay develop before math self-concepts, and (b) implicit stereo-types and implicit self-concepts may precede explicit ones. In partfor these reasons, this would translate to an expectation that theimplicit—explicit correspondence will be weak for stereotypemeasures (if implicit stereotypes are evident before their explicitcounterparts are) and nonexistent for math self-concept measures(if neither implicit nor explicit math self-concepts are in place atages at which stereotypes are already evident). The current studyprovides relevant data.

Parental Beliefs and Practices About Mathematics

Parental involvement in mathematical practices at home hasbeen studied as another potential contributor to children’s beliefsabout, and achievement in, mathematics (Kleemans, Peeters,Segers, & Verhoeven, 2012; Levine, Suriyakham, Rowe, Hutten-locher, & Gunderson, 2010; Manolitsis, Georgiou, & Tziraki,2013). The activities in which parents engage with their children athome may communicate beliefs and expectations held by theseparents regarding their children and mathematics (Eccles, 1983).Specifically, activities and gender labeling in home interactionsmay serve to reinforce the pervasive views—either parents’ per-sonally held beliefs or societal stereotypes—about which activitiesand domains are more appropriate “for boys” versus “for girls”(Coyle & Liben, 2016; Leaper & Farkas, 2015; Martin & Halver-son, 1981; Simpkins, Fredricks, & Eccles, 2015).

Parents who have positive beliefs about their child doing math-ematics and/or have more positive math self-concepts themselves,tend to engage in higher frequency of mathematics-related activ-ities at home (Gunderson et al., 2012). Parents of prekindergar-teners who report enjoying doing mathematics with their childrenengage more often in numeracy practices at home (Blevins-Knabe,Austin, Musun, Eddy, & Jones, 2000), and parents who havehigher expectations about the importance of mathematical skillsfor their children’s success in first grade report a higher frequencyof home numeracy practices (del Río, Susperreguy, Strasser, &Salinas, 2017; Skwarchuk, Sowinski, & LeFevre, 2014). Similarly,parents who possess stronger math self-concept report higherexpectations for their children’s mathematical skills, thus engagingwith them more frequently in numeracy activities at home, com-pared to parents with weaker math self-concepts (Simpkins,

Fredricks, & Eccles, 2012). Research has also shown that motherswho are more confident about their mathematical skills are betterat conveying mathematical content and scaffolding their child’slearning during homework (Caspe, Woods, & Lorenzo Kennedy,2018; Hyde, Else-Quest, Alibali, Knuth, & Romberg, 2006).

Parents’ stereotypes could also influence their differential en-gagement in mathematical activities with their sons and daughters.In many Western countries, there is a stereotype held by adults thatmathematics is a male domain (e.g., Leslie, Cimpian, Meyer, &Freeland, 2015; Nosek et al., 2009). Research on the intergenera-tional transmission of beliefs suggests that children’s own beliefsabout mathematics may arise at least in part as a function of theirparents’ beliefs and stereotypes (Berkowitz et al., 2015; Pruden &Levine, 2017; Upadyaya & Eccles, 2015). This is in line with theresults of a meta-analysis investigating parents’ and children’sgender schemas, which showed that parents who had a moretraditional gender schema had children with gendered cognition ofthemselves and others (Tenenbaum & Leaper, 2002). Parents whohold more firmly rooted math–gender stereotypes are more likelyto explain science to their sons than to their daughters, and also usemore cognitively demanding speech with their sons than with theirdaughters (Crowley, Callanan, Tenenbaum, & Allen, 2001; Tenen-baum & Leaper, 2003).

To date, research on parental involvement and parents’ beliefshas typically relied on maternal data only (Tracey & Young,2002). There is an increasing call for the inclusion of fathers, andnot only mothers, to illuminate more fully the role of the homeenvironment and parenting factors on children’s mathematicaloutcomes (e.g., Bhanot & Jovanovic, 2005, 2009; Jacobs &Bleeker, 2004). To our knowledge, only two studies have exam-ined both fathers’ and mothers’ beliefs about mathematics withchildren as young as 5- to 6-years-old. Tomasetto, Mirisola, Galdi,and Cadinu (2015) found that the relation between fathers’ eval-uation of their child’s mathematical ability and child’s own self-perception of ability remained significant even after controlling forthe effect of mother’s evaluation. A study by del Río and col-leagues (2017) found that—although both maternal and paternalnumeracy expectations were related to mathematical practices athome with their kindergarten children—only maternal practicespredicted children’s numeracy outcomes. In the current study, weare examining how both mothers’ and fathers’ beliefs and practicesabout mathematics are related to children’s math self-concept, andwhether mothers’ and fathers’ involvement may be differentiallyassociated with their sons’ and daughters’ beliefs. Because tradi-tional gender roles within Latino families are known to contributeto shaping children’s beliefs (Rivas-Drake & Marchand, 2016), weinvestigate statistical path models involving differential links be-tween maternal and paternal beliefs and practices and children’smath self-concepts.

SES and Individual Differences in Math Self-Concepts

SES has been shown to be associated with early mathematicalskills in young children (Dearing et al., 2012; Galindo & Sonnen-schein, 2015; Melhuish et al., 2008). The quality of the homelearning environment is related to the availability of educationalresources and children’s academic performance (Fan & Chen,2001; Jeynes, 2005). SES is also a significant predictor of families’involvement in different kinds of numeracy activities with their

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3KINDERGARTENERS’ BELIEFS ABOUT MATHEMATICS

children: It has been reported that low SES families tend to offerfewer numeracy activities and resources (Saxe et al., 1987; Sus-perreguy & Davis-Kean, 2016). This difference in home numeracyactivities may be related to both the development of mathematicalskills and of mathematical beliefs such as stereotypes or self-concepts.

Another pathway through which SES may be related to chil-dren’s own views of mathematics is through societal expectations.In Chile, schools are highly segregated by SES and thus studentsare grouped in homogeneous schools. The educational results ofeach school sector (public, charter, and private) on the Chileanstandardized tests show an important gap between low and highSES schools. The scores of schools on the standardized tests ofmathematics and language in Chile (SIMCE) are public, andannual rankings of schools are published in the newspapers. Con-sequently, Chilean families and children from different neighbor-hood schools are well aware of social expectations regarding theireducational achievement, putting students from a low SES back-ground at risk of being susceptible to these expectations from anearly age.

Several studies have shown that parental expectations are re-lated to an increase in students’ mathematical achievement, andthat SES can be a moderator of these relations (Murayama, Pekrun,Suzuki, Marsh, & Lichtenfeld, 2016; see also Benner, Boyle, &Sadler, 2016; Bicer, Capraro, & Capraro, 2013; Stull, 2013). Usingstructural equation modeling techniques and data from a nationalcross-sectional study, Davis-Kean (2005) found that SES was apredictor of parental expectations, and that these expectations, inturn, are related to achievement through parents’ practices. In otherwords, low SES families showed lower expectations and, conse-quently, parents demonstrated less supporting academic practices.

Aims of the Current Study

It is informative to examine the developmental relation betweenchildren’s math stereotypes and their math self-concepts; and it isalso important to additionally examine the interplay between pa-rental beliefs and practices and their relations to the developmentof children’s own beliefs.

To address this point, we used path analysis, a technique thatallows the examination of multiple pathways simultaneously toidentify both direct and indirect effects of predictors. This pathanalysis was conducted to assess several theoretical predictionsthat are derived from the five interrelated lines of previousresearch. First, capitalizing on research in elementary studentsthat shows that children hold stereotypes about which gender ismore strongly associated with mathematics (Ambady et al.,2001; Cvencek et al., 2011; Galdi et al., 2014; Heyman &Legare, 2004; Steele, 2003), we examined the possible relationof children’s own stereotypes about mathematics and gender totheir emerging math self-concept. For consistency, we alsoexamined whether parents’ stereotypes were associated withparents’ self-concepts. Second, following research about therelation of parents’ beliefs and their engagement in mathemat-ical activities with their children (Blevins-Knabe et al., 2000;del Río et al., 2017; Gunderson et al., 2012; Hyde et al., 2006;Simpkins et al., 2012; Skwarchuk et al., 2014), we examinedpaths from parents’ beliefs, stereotypes, and self-concepts, totheir mathematical practices at home. Third, based on findings

that parents with more traditional gender schema had childrenwith gendered cognition of themselves and others (Tenenbaum& Leaper, 2002), we also evaluated the relations of parents’self-concepts to children’s self-concepts and stereotypes.Fourth, given the known association of SES with mathematicsachievement and the mathematical home environment (Dearinget al., 2012; Fan & Chen, 2001; Galindo & Sonnenschein, 2015;Jeynes, 2005; Melhuish et al., 2008; Saxe et al., 1987; Susper-reguy & Davis-Kean, 2016), we also examined the role of SES.Fifth, taking into account the part that traditional gender rolesmay play in differentiating parents’ behaviors toward their sonsversus daughters (Rivas-Drake & Marchand, 2016), we exam-ined the above-mentioned relations for both mothers’ and fa-thers’, and took into account the child’s sex. Some of thesemodels are causal in nature, but the path analyses themselves donot provide clear evidence of causal direction (we return to thisissue in the Discussion section).

Such messages are likely to be related to a child’s motivationto pursue particular activities in the short run. In addition, overtime, children are expected to develop their own self-perceptions and interests, based on their parents’ messages andbehaviors as well as on their own experiences, and these self-perceptions will ultimately affect their future task choices (Ja-cobs & Eccles, 2000). For example, parents who value math andbelieve that their children excel at it might convey this to thechild by engaging in a range of math-promotive behaviors (e.g.,positive comments, playing math games with the child, enroll-ing the child in an engineering camp). Such messages are likelyto help children develop high values and more positive self-perceptions of math abilities. Of course, it is important toacknowledge that parents’ and children’s beliefs are likely toinfluence each other reciprocally.

Beyond the path analysis, we sought to make three novelcontributions. First, we measured both explicit and implicitbeliefs in the same children, thus providing a more comprehen-sive assessment of children’s developing beliefs about mathe-matics than either type of measure taken alone. Based on theextant literature, we expected to find significant relations be-tween these variables in the case of implicit measures (but didnot predict this for the explicit, self-report measures becauseprevious work found them to be less sensitive in preschoolchildren). Second, few previous studies of young children haveexamined the relation between children’s math– gender stereo-types and self-concepts and the corresponding measures in bothparents. This is an important gap because parents are likely tobe a strong source of identity development in children, andmothers and fathers might have distinct roles. We hypothesizeddifferential links between parental beliefs and practices andchildren’s math self-concept, depending on the gender of theparent and the child. Third, no previous study has examined theearly development of math– gender stereotypes and their rela-tion to children’s math self-concepts as early as 5 years of age.At the broadest level, this study aimed to examine the relationbetween parents’ and children’s beliefs about mathematics inthe family environment, especially as it pertains to the emer-gence of students’ math self-concept at early ages. Based onprevious literature with older children, we expected math–gender stereotypes to emerge earlier and influence math self-concepts rather than the other way around.

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4 DEL RÍO ET AL.

Method

Participants and Setting

The data reported in this study were collected between Marchand June of 2016, using a sample of 5-year-old children and theirparents in Chile. The procedures of this research were approved inadvance by both the Santiago School District, as well as theUniversity Diego Portales institutional ethics committee, as project#067–2014, “La matemática es un asunto de niños: estereotipos deniños y niñas de kínder, sus familias y educadoras” [“Math is forboys: Kindergarten children, teacher and parents math-genderstereotypes,” Fondecyt N°1150156]. Recruitment was donethrough schools. Principals were contacted by phone and then inperson to explain the procedures of the study. Parents were con-tacted during Parent–Teacher Association meetings to explain thestudy procedures, and they were asked to give written consent fortheir participation and that of their children.

The study was conducted in eight urban schools in Santiago,Chile, four of which were public schools that primarily servedstudents from low-income families, and the other four were privateschools that served children from higher income families. There ishigh socioeconomic segregation within the Chilean educationalsystem (Valenzuela, Bellei, & de los Ríos, 2014), which meansthat, in any given school, children’s SES will be very similar. Also,we used household income declared by parents as an individualmeasure for children’s SES (low SES families came from house-holds that are actually considered to be low-income by Chileanstandards).

Children. Our sample included 180 kindergarten children (87girls). Kindergarten is the first mandatory educational level inChile, and the last before formal education that begins with 1stgrade. The mean age of children was 5.6 years (SD � 0.37, agerange � 4.4–7.1 years). Children’s age was not significantlydifferent between low and high SES. Children were evaluatedduring a one-on-one session with a researcher in a quiet roomprovided by the schools. All children gave verbal assent to partic-ipate. The measures were administered in a single session lasting20–30 min. Children were tested individually in a separate quietroom outside of their classroom while seated at a desk.

Parents. One hundred eighty families (99 from low SES, 81from high SES) were recruited. Each family included a participantchild plus two parental figures. The mother’s and father’s ageswere: mother age, M � 36.3 years, SE � 6.8; father age, M � 38.9years, SE � 8.5. On average, low SES parents had an educationallevel lower than a high school diploma, whereas high SES parentswere above a high school diploma. The father group included notonly biological fathers, but also encompassed male father figuresliving in the homes of the targeted children, including grandfa-thers, male partners, and adult brothers (19 cases). The parents’evaluation was done at their home, and a small monetary incentive(equivalent to U.S. $30) was offered for their participation. Out ofthe total 180 children and their parents, 171 (82 female) presentedcomplete data on all tasks, and these families constituted theanalytical sample of this study.

Materials

Each test session began with a 3–5 min description of the study,during which children were familiarized with the test apparatus

(i.e., electronic tablet with a 20.3 cm screen). The children weretold that they would be “asked to play a computer game and toanswer some questions.” For both children and parents, the orderin which implicit and explicit measures were administered wascounterbalanced. The numeracy beliefs and practices questionnairewas administered to parents after the implicit and explicit mea-sures.

Children’s tasks. All children completed two implicit andtwo explicit measures.

Implicit measures. For the implicit tasks, children completeda child-friendly adaptation of the adult IAT. The child-friendlyadaptations of the IAT used in this research (described below)were based on a pictorial, color-coded Child IAT version devel-oped and validated for use with preschool children (see Cvencek,Greenwald, & Meltzoff, 2016, for details). Children are asked torapidly sort the stimuli belonging to four categories by using tworesponse keys. The Child IAT is based on the principle that it iseasier to give the same response to items that are associated thanif they are not. Children, similarly to adults, find certain associa-tions to be more natural or “congruent,” and they respond to themwith more facility.

Implicit measure of math–gender stereotypes. This Child IATmeasure assessed the stereotype of associating social group withacademic subject (math � boys). This is referred to as a math–gender stereotype. During the math–gender stereotype Child IAT,children responded to images representing the categories of math,reading, boy, and girl. The math and reading categories were eachrepresented by pictures of items related to the subjects (e.g.,calculator, numbers, book, and letters). Four pictures of childrenwere used to represent each of the two gender categories. In onetask, math and boy images shared a response key, as did readingand girl images. This is termed the “congruent” task because italigns with the common stereotype. In the other task, the assign-ment of the math and reading images was reversed.

The math–gender stereotype Child IAT score (D) was calcu-lated using the scoring algorithm developed by Greenwald, Nosek,and Banaji (2003), where D score is calculated by first (a) com-puting the difference between the mean response latencies of thecongruent and incongruent tasks for each subject, then (b) dividingthat by the pooled standard deviation. For the math–gender ste-reotype IAT, D was scored so that it had the computational upperand lower bounds of �2 (math � boys) to �2 (math � girls), witha rational value of 0 indicating an equally strong association ofmath with both genders (i.e., a D score of 0 indicated the child’smean response latency in the math � boys task was statisticallyequal to that of the math � girls task).

Implicit measure of math self-concept. The implicit measureof math self-concept was another Child IAT. This measure as-sessed the degree to which the child associated him- or herself withmath (me � math). The math self-concept measure followed thesame format as the math–gender stereotype IAT, with one excep-tion: Instead of the boy and girl categories, the categories me andnot-me were included, along with math and reading. The me andnot-me categories were represented by two sets of novel flags: oneset that had been given to the child (“my flags”), and another setwhich did not belong to the child (“not my flags”). This is basedon a social psychology phenomenon termed the mere ownershipeffect. Children, just like adults, who receive an item as a gift (i.e.,acquire its ownership) evaluate that item more favorably than do

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5KINDERGARTENERS’ BELIEFS ABOUT MATHEMATICS

people who examine an identical item but do not own it (Beggan,1992). Cvencek et al. (2016) provide extensive psychometric val-idation of the use of small flags as proxies for the self in Child IATmeasures. In one test block, math and me images shared a responsekey, as did reading and not-me images. In the other test block, leftversus right assignment of the math and reading images wasreversed.

The math self-concept Child IAT D was computed in a similarfashion as the math–gender stereotype measure, with the compu-tational upper and lower bounds of �2 (me � math) to �2 (me �reading), with a rational value of 0 indicating an equally strongassociation of self with both academic subjects (i.e., a D score of0 indicated the child’s mean response latency in the me � mathtask was statistically equal to that of the me � reading task).

Explicit measures. For the explicit tasks, children completedtwo pictorial Likert-scales. The explicit measures of math–genderstereotypes and math self-concepts were administered as fourLikert-scale questions based on Harter and Pike’s (1984) PictorialScale of Perceived Competence and Acceptance for Young Chil-dren. Cvencek et al. (2011) validated these pictorial measures asindicators of math–gender stereotypes and math self-concepts (seealso Cvencek et al., 2015; Paz-Albo Prieto, Cvencek, Llácer,Escobar, & Meltzoff, 2017).

Measures assessing each of the two constructs consisted of twoquestions. For each question, children were shown two pictures ofa child character and responded by reporting: (a) which of the twocharacters (boy or girl) they believed possessed an attribute (e.g.,liking math) to a greater degree, and (b) whether the characterpossessed the attribute “a little” or “a lot.” This was done bypointing to two different-sized circles (1.1 cm and 2.3 cm indiameter, respectively) to indicate less versus more possession ofthe attribute.

Explicit measure of math–gender stereotypes. The self-reportmeasure of math–gender stereotypes was administered as twoLikert-scale questions. In one item, a picture of a boy doingmathematics was presented next to a picture of a girl doingmathematics, and the child was asked which one was believed tolike math more. After making a selection, the child was asked todecide if the character in the picture liked math a little more or alot more. A second item followed the same format as the first item,but the characters in the pictures were reading instead of doingmathematics; the children were asked to decide who liked to readmore. The explicit math–gender stereotype measure was com-puted as a difference score that ranged from �2 (“boy characterlikes math more than he likes reading”) to �2 (“girl character likesmath more than she likes reading”), with a rational value of 0indicating that the child picked the boy and girl character as bothliking math (and reading) equally (in increments of .5).

Explicit measure of math self-concept. The self-report mea-sure of math self-concept was similar to the pictorial math–genderstereotype measure. For each question, children were shown twopictures of a child character—one engaged in mathematics, theother in reading—and responded by selecting which same-sexcharacter was more like the self. The explicit math self-conceptmeasure was scored as a difference score that ranged from �2(“same-sex character doing math is more like me”) to �2 (“same-sex character doing reading is more like me”), with a rational valueof 0 indicating that the child picked the same-sex character that

was doing mathematics and the same-sex character that was doingreading as both being equally like him or her (in increments of .5).

Parents’ tasks. Parents completed the corresponding adultversions of implicit and explicit stereotype and self-concept mea-sures as their children, as well as explicit measures of homenumeracy practices and beliefs.

Implicit measures. For the implicit tasks, parents completedtwo standard, adult IATs: One IAT measured math–gender ste-reotypes and another IAT measured math self-concepts. Bothimplicit measures were derived from previously published IATswith adults (Nosek, Banaji, & Greenwald, 2002) and used the samescoring conventions as the corresponding Child IATs (see above).

Implicit measure of math–gender stereotypes. The implicitmeasure of math–gender stereotype for parents was an IAT withthe same categories as the math–gender stereotype Child IAT, butwith the following, written category labels: mathematics, lan-guage, male, and female. Where the Child IAT used pictures torepresent the four categories, the adult IAT used only text stimuli(e.g., “subtraction,” “verbs,” “him,” “she”). The math–genderstereotype IAT for parents was scored using the same D scoringalgorithm that was used with children (Greenwald et al., 2003).

Implicit measure of math self-concept. The implicit measureof math self-concept for parents was an IAT with the same cate-gories as the math self-concept Child IAT, but with the following,written category labels: mathematics, language, self, and other.Where the Child IAT used pictures to represent the four categories,the adult IAT used only text stimuli (e.g., “algebra,” “poetry,”“myself,” “them”). The D scoring algorithm used for the math–gender stereotype IAT was also used to score the math self-concept IAT for parents (Greenwald et al., 2003).

Explicit measures. Parents also completed three explicit mea-sures pertaining to math–gender stereotypes, math self-concepts,and parental numeracy expectations and practices.

Explicit measure of math–gender stereotypes. The self-reportmeasure of math–gender stereotype for parents was administeredas two Likert-scale questions, one each for mathematics and lan-guage: “Please rate how much you associate mathematics [lan-guage] with males or females” (Nosek et al., 2002). Responseswere selected from a scale of 1 (strongly male) to 7 (stronglyfemale), with a midpoint option of 4 (neither male nor female).Following Nosek et al. (2002), by taking the difference betweenthe mathematics and language ratings, the explicit stereotype mea-sures were made comparable to the implicit measures: Rationalzero points were provided by the measures’ construction as dif-ference scores that have expected values of zero when the con-structs being measured are absent.

Explicit measure of math self-concept. The self-report mea-sure of math self-concept for parents was administered as threeLikert-scale questions (Nosek et al., 2002). Two questions askedhow much the subject agreed with the statements, “I considermyself to be a mathematical [language] person. (Me considero amí mismo/a como una persona matemática [de lenguaje]).” Re-sponses were selected from a scale of 1 (strongly disagree) to 7(strongly agree), with a midpoint option of 4 (neither disagree noragree). A third item asked, “Do you consider yourself to be moremathematical or linguistic? (¿Se considera a sí mismo como másmatemático/a o más de lenguaje?).” Responses for this item wereselected from 1 (strongly a mathematical person) to 7 (strongly alanguage person), with a midpoint option of 4 (neither a mathe-

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6 DEL RÍO ET AL.

matical nor a language person). Similar to the math–genderstereotype measure, the explicit math self-concept measure wasalso computed as a difference score between mathematics andlanguage ratings.

Home numeracy expectations and practices questionnaire.Both parents also completed an adapted Spanish version of theParents’ Home Numeracy Questionnaire on paper (Skwarchuk etal., 2014). This questionnaire included a series of home numeracyactivities in which parents reported the frequency with which theyinvolved their children in mathematical practices at home, on ascale ranging from 1 (rarely or never) to 5 (most days per week).Some sample items include, “I help my child learn simple sums(e.g., 2 � 2),” “I encourage my child to do mathematics in his/herhead,” “We talk about time with clocks and calendars,” and “I helpmy child weigh, measure, and compare quantities;” and also ac-tivities such as, “I teach my kid to recognize written numbers,”“We play board and card games,” or “We sing songs that includenumbers.” Two scales, one for mothers and one for fathers, werecreated by averaging the 13 items for each parent.

Parents also reported how much they agreed with the impor-tance of their child reaching specific numeracy benchmarks beforestarting Grade 1, on a scale of 1 (unimportant) to 5 (important).These benchmarks included counting to 10 and counting to 100,among others. Following Skwarchuk et al. (2014), parents indi-cated the importance of six numeracy benchmarks. The resultingratings were averaged to create the mothers’ and the fathers’numeracy expectations scales.

Data Reduction

Based on the three previously published exclusion criteria fromthe Child IAT literature (i.e., excessively fast or slow responding,excessive error rates; Cvencek et al., 2011), data for 17 participantswere excluded from the analyses. The final sample included 163children (80 girls; 83 boys) who had valid data for at least one ofthe two Child IATs (none of the parents met any of these exclusioncriteria). For the path analyses, missing data were treated usingFull Information Maximum Likelihood in Mplus, which providesunbiased estimates in these cases (Graham, 2009). Therefore, thefinal sample for these models was 171 cases (82 mothers and 89fathers).

Analysis Plan

First, we examined the means of the implicit and explicit mea-sures. Scores for each group of participants (girls, boys, mothers,and fathers) were compared against its neutral point. For allimplicit measures, the neutral point was the rational zero point ofeach Child/adult IAT; for all explicit measures the neutral pointwas the midpoint of the scale (see above). Testing for the signif-icant differences from zero allows us to evaluate whether math–gender stereotypes and math self-concepts are evident in eachgroup of participants and if so, in which direction. In the case ofchild participants, these tests provide developmental evidence forthe emergence (or lack thereof) of implicit and explicit math–gender stereotypes and math self-concepts at 5 years of age.

In addition, for each measure, we compared boys’ scores togirls’ scores, and mothers’ scores to fathers’ scores. Testing formale–female differences in math–gender stereotypes and math

self-concepts for children and parents allows us to evaluatewhether the construct (stereotype vs. self-concept) is evident inone gender more strongly than in the other.

Next, we examined correlations between children’s and parentalscores on all measures. Testing for parent–child relations allows usto evaluate how stereotypes about mathematics may transfer fromparents to children.

Finally, we conducted path analyses to provide estimates of themagnitude and significance of hypothesized relations between ourmeasured variables. Using path analyses with Mplus (Muthén &Muthén, 1998–2015), we tested models for predicting children’sexplicit and implicit math self-concepts. These models allow us toevaluate how well the proposed cognitive, parental, behavioral,and demographic factors predict math self-concepts of 5-year-olds.

Results

The results are organized in five sections. Presented first are theresults of implicit and explicit stereotype measures, followed bythe results of implicit and explicit math self-concept measures.Presented next are the analyses of the explicit measures of parentalnumeracy beliefs and practices at home. Finally, the full models ofdirect and indirect effects on children’s early implicit math self-concepts are presented. Table 1 shows correlations between SES,child gender, and our child and parent measures (the correlationtable that presents these results separately for girls and boys can befound in the online supplemental material).

Math–Gender Stereotypes

On the IAT measure, the implicit math � male stereotype wassignificantly different from zero (and in the predicted, stereotypicdirection of math � male) for fathers, t(170) � 6.79, p � .001, d �0.52, mothers, t(170) � 6.53, p � .001, d � 0.50, and boys,t(80) � 2.62, p � .01, d � 0.29, but not for girls, p � .66 (seeFigure 1, top panel). There was a sex difference in how stronglythe children held the math–gender stereotype: Boys associatedmath with male significantly more strongly than did the girls,t(156) � 2.02, p � .04, d � 0.32. No statistical difference wasfound for the strength of the implicit math–gender stereotype formothers and fathers, p � .94.

On the explicit measure, the math � male stereotype wasstatistically significant (again in the stereotypic direction) forfathers, t(170) � 5.98, p � .001, d � 0.46, and mothers, t(170) �8.52, p � .001, d � 0.65, but the explicit measure was notsignificant among either the kindergarten boys or the kindergartengirls, ps � .40 (see Figure 1, bottom panel). No differences in thestrength of the stereotype were found between explicit math–gender stereotypes of mothers and fathers, p � .12, nor betweenboys and girls, p � .61. However, we found that mothers of boyshad stronger explicit math–gender stereotypes than fathers ofboys, t(88) � 2.47, p � .02, d � 0.35.

Math Self-Concepts

The math self-concept measures addressed how the individualparticipant identified with mathematics. On the implicit mathself-concept measure, the me � math association was significantlydifferent from zero for fathers, t(170) � 5.30, p � .001, d � 0.41,

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7KINDERGARTENERS’ BELIEFS ABOUT MATHEMATICS

approached significance for kindergarten boys, t(81) � 1.73, p �.09, d � 0.19, but was clearly not significant for mothers or forkindergarten girls, ps � .96 (see Figure 2, top panel). Fathers hadsignificantly stronger implicit math self-concepts than mothers,t(170) � 3.99, p � .001, d � 0.41. No statistical difference wasfound between implicit math self-concepts of boys and girls, p �.22.

On the explicit math self-concept measure, the me � mathassociation was significantly different from zero in the positivedirection for fathers, t(170) � 5.02, p � .001, d � 0.38, and theme � math association was statistically significant from zero inthe negative direction for mothers, meaning that they identifiedsignificantly more strongly with linguistics than with math,t(170) � �3.60, p � .001, d � �0.28 (see Figure 2, bottompanel). As expected, fathers identified with mathematics signifi-cantly more strongly than mothers, t(170) � 6.13, p � .001, d �0.66. For both boys and girls, the explicit math self-concept wasnot significantly different from zero, ps � .70. The differencebetween boys’ and girls’ explicit math self-concepts was notsignificant, p � .71.

Parental Numeracy Practices and Parental NumeracyBeliefs

On the parental measure of numeracy practices at home, bothmothers and fathers reported a mean frequency of home numeracypractices greater than the scale midpoint, ts � 3.12, ps � .002,ds � 0.24 (see Figure 3). Mothers reported that they were involvedin numeracy practices with their child significantly more fre-quently than fathers did, t(169) � 4.18, p � .001, d � 0.39. Nosignificant differences were observed for mother or father prac-tices in relation to children’s gender (p � .16, for mothers; p �.90, for fathers).

On the parental measure of numeracy expectations, mothersand fathers both reported an importance of numeracy signifi-cantly higher than the scale midpoint, ts � 2.31, ps � .03, ds �

0.17 (see Figure 3). There was no significant difference be-tween mothers’ and fathers’ beliefs of how important numeracywas for their children before starting first grade, p � .12.

Path Analyses

We tested models to explain children’s math self-concept. Pre-dictors of the child’s self-concept were child stereotype, householdincome declared by parents (SES), parents’ home numeracy prac-tices, and parents’ math self-concepts. Parents’ math self-conceptswere also entered as predictors of child stereotype. Parents’ nu-meracy beliefs, their stereotypes, and their self-concepts wereentered as predictors of their home numeracy practices and SES,and the parents’ math–gender stereotypes were entered as predic-tors for their self-concepts.

Fit was assessed by using the three most commonly recom-mended fit indices (Hu & Bentler, 1999). As recommended(Jackson, Gillaspy, & Purc-Stephenson, 2009; Klem, 2000; Yu,2002), a good fit was indicated by three preliminary tests. First,a good fit was indicated by having a chi-square (�2) value thatwas not statistically significant. Second, the Root mean squareerror of approximation (RMSEA; a measure based on the non-centrality parameter) should have values less than 0.10 toindicate adequate model fit for RMSEA, or values around .06 toindicate good or excellent fit (Hu & Bentler, 1999). Third, thecomparative fit index (CFI) was used, because— unlike some ofthe less restricting indices—it pays a penalty for every estima-tion parameter added. CFI values greater than 0.85 indicateacceptable model fit (Bollen, 1989; Watkins, 1989). Both mod-els (i.e., using both implicit and explicit measures) met thesethree criteria and thus are reported here.

The fit of the model with implicit measures was good (�2 �64.53, df � 54, p � .16; RMSEA � 0.048; CFI � 0.915).Importantly, it showed significant paths to implicit math self-concept of children. The model (see Figure 4) revealed that

Table 1Correlations (Pearson’s R) for SES, Gender, and All of the Children’s and Parents’ Implicit and Explicit Measures

Measure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1. SES —2. Child’s gender �.02 —3. Child’s Im. MGS �.11 .16� —4. Mother’s Im. MGS �.12 �.04 �.10 —5. Father’s Im. MGS .002 �.002 .03 �.06 —6. Child’s Ex. MGS .08 �.04 �.10 �.08 �.02 —7. Mother’s Ex. MGS .08 .09 �.14 .17� �.11 �.10 —8. Father’s Ex. MGS .11 �.09 �.03 �.02 .20�� .13 �.001 —9. Child’s Im. MSC .13 .10 �.02 �.11 �.07 �.04 �.01 .06 —

10. Mother’s Im. MSC .18� .06 .02 �.30�� .13 .06 �.04 .17� .10 —11. Father’s Im. MSC .28�� �.02 .03 .03 .27�� �.03 .05 .10 �.12 .09 —12. Child’s Ex. MSC .01 .03 �.02 �.14 �.13 .03 �.03 �.14 .14 .07 .01 —13. Mother’s Ex. MSC .14 �.03 �.17� �.21�� �.003 .15 �.16� .003 .08 .29�� �.08 .12 —14. Father’s Ex. MSC .28�� �.05 �.05 �.01 .11 .10 �.03 .13 �.05 .02 .20�� �.04 .02 —15. Mother’s NP �.20�� �.11 �.08 .14 �.06 .01 �.02 �.02 �.09 �.15� �.02 .08 �.07 �.05 —16. Father’s NP �.17� �.01 .0001 .10 .15� �.06 .14 �.04 .07 �.12 �.01 .05 �.11 .05 .26�� —17. Mother’s NB �.05 .03 .04 .05 .07 .06 .01 .08 �.01 �.03 �.03 .05 .12 .04 .35�� .26�� —18. Father’s NB �.09 �.02 .05 .07 .07 .04 .10 �.05 �.06 �.12 .01 .09 �.03 .10 .19� .42�� .39��

Note. SES � socioeconomic status; Ex. � explicit; Im. � implicit; MGS � math–gender stereotype; MSC � math self-concept; NP � numeracypractices; NB � numeracy beliefs.� p � .05. �� p � .01.

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8 DEL RÍO ET AL.

girls’ math self-concept was directly related to SES (girls fromhigh SES have higher math self-concept than girls from lowSES) and related to their fathers’ and mothers’ math self-concepts. Fathers’ math self-concept (the degree to which theyself-identified with mathematics) had a significant negativepath to their daughters’ math self-concept (B � �0.35, p �.001), while the path of mothers’ self-concept was positive fordaughters (B � 0.20, p � .01). In addition, the frequency withwhich fathers engage in home numeracy activities with theirdaughters had a significant positive effect on their daughters’math self-concept (B � 0.29, p � .03). Surprisingly, mothers’math self-concept had a negative effect on their involvementwith mathematical activities with their daughters (B � 0.24,p � .02). In the case of boys, none of the variables in the modelaccounted for significant variance in their math self-concept. Todetermine whether girls’ and boys’ models were significantly

different, we fitted a model in which all predictors of childself-concept were constrained to be equal for boys and girls (seeKlem, 2000). This model had significantly worse fit than themodel where predictors of self-concept were allowed to varybetween boys and girls (��2 � 12.87, df � 6, p � .04).

The fit of the model with explicit measures was also good, butin this case, the constrained model (in which paths are set to beequal for boys and girls) and the unconstrained model (in whichthey are allowed to vary across genders) had similar fit (��2 � 4.1,df � 6, p � .05). Although the constrained model was slightlymore parsimonious, we report the unconstrained model in the maintext (for completeness, the constrained explicit model is reportedin the online supplemental material) so that it can be compared tothe (unconstrained) implicit model. The fit of the unconstrainedmodel (see Figure 5) was good (�2 � 58.69, df � 54, p � .31;

Figure 1. Implicit (top) and explicit (bottom) math–gender stereotypes ofChilean 5-year-old children and their parents. Asterisks above a bar indi-cate difference from the neutral value of zero. Asterisks above a bracketindicate male-female difference. � p � .05. ��� p � .001. Error barsrepresent SEs.

Figure 2. Implicit (top) and explicit (bottom) math self-concepts ofChilean 5-year-old children and their parents. Asterisks above a bar indi-cate difference from the neutral value of zero. Asterisks above a bracketindicate male-female difference. a p � .01. ��� p � .001. Error barsrepresent SEs.

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9KINDERGARTENERS’ BELIEFS ABOUT MATHEMATICS

RMSEA � 0.032; CFI � 0.942). However, there were no signif-icant contributions to the child’s explicit math self-concept for anyof the gender groups which may explain why the constrained andunconstrained models function equally well.

Discussion

This study systematically tested 5-year-old children’s beliefsabout mathematics by examining: (a) children’s stereotypes andmath self-concept, (b) parental math–gender stereotypes and mathself-concept, (c) parental beliefs about the importance of mathe-matics and their home numeracy practices (expectations), and (d)family SES. Several significant results emerged that are relevant totheories about STEM learning and stereotypes, the intergenera-tional transfer of beliefs, identity development, and home prac-tices.

First, sex differences were found on implicit measures of kin-dergarteners’ math–gender stereotypes (with boys holding themath � boy stereotype significantly more strongly than girls).Second, both mothers and fathers demonstrated highly significantmath–gender stereotypes, and fathers held the me � math self-concept more strongly than mothers. Third, girls’ implicit mathself-concept was linked directly to their family’s SES and parents’math self-concepts. Significant indirect paths from parents’ genderstereotypes to children’s self-concepts were observed for the fa-thers of daughters.

Children’s Early Math–Gender Stereotypes and MathSelf-Concepts

As early as kindergarten, Chilean boys already demonstrateimplicit math–gender stereotypes. This finding contributes novelinformation to the literature. First, it is the earliest demonstrationof implicit math–gender stereotypes to date. Previous researchwith elementary-school students in the United States (Ambady etal., 2001; Cvencek et al., 2011), Canada (Steele, 2003), and Italy(Galdi et al., 2014) showed later emergence for this stereotype.

Figure 3. Numeracy practices at home and beliefs about the importance ofnumeracy of Chilean mothers and fathers. Asterisks above a bar indicatedifference from the midpoint. Asterisks above a bracket indicate male–femaledifference. � p � .05. �� p � .01. ��� p � .001. Error bars represent SEs.

Figure 4. Conceptual model of implicit math self-concept for girls and boys and standardized coefficients forthe final (unconstrained) model. Standardized coefficients for girls are outside the parentheses; standardizedcoefficients for boys are inside the parentheses. � p � .05. �� p � .01.

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10 DEL RÍO ET AL.

The early emergence of the math–gender stereotype in Chileanboys makes sense because the data show that the adult stereotypesand the gender gaps in children’s standardized mathematicsachievement (assessed in Grade 8 and 11) are more pronounced inChile than in the United States, Canada, and Italy (Nosek et al.,2009). The current study shows that in a culture with large andpersistent gender gaps in mathematics (one of our motivations forselecting Chile as a testbed), implicit math–gender stereotypesmay be acquired as early as 5 years of age.

Second, boys, but not girls, demonstrated a significant math–gender stereotype. It is also true in North American samples thatthe math–gender stereotypes are more pronounced in males than infemales (Nosek et al., 2009). In the three available studies withimplicit stereotype data (Ambady et al., 2001; Cvencek et al.,2011; Steele, 2003), more than 83% of K–2 boys demonstratedimplicit math–gender stereotypes, in contrast to approximately56% of K–2 girls. In the current study sampling much youngerchildren, the percentage of children who demonstrated the implicitmath–gender stereotype was also higher for boys (65%) than forgirls (44%) at age 5. Why would boys be more prone to adopt thesestereotypes at such an early age? One possible explanation issuggested by gender schema theory (Martin & Halverson, 1981).The overall schema guides cognitive processing of gender infor-mation by providing children with information—at the level oflabels (e.g., “for boys”)—about what kinds of activities are mostsuitable for each gender. If parents and the wider culture stronglyhold the pervasive stereotype that mathematics is “for boys” andlabel a variety of activities involving numeracy as being for males,then children who identify with being a boy may naturally registerthis stereotype and over the course of development begin applyingthis stereotype to themselves.

Third, we speculate that the prominent societal stereotype thatmathematics is for boys more than for girls is registered at a veryyoung age perhaps through some form of “statistical learning”about regularities in the ambient environment. Thus, in terms ofdevelopmental order of acquisition, we believe that math–genderstereotypes are acquired before math self-concepts—childrenseem first to register the regularities exhibited in the culture abouttheir social group (stereotypes) and then, over the course of de-velopment, to internalize them by applying these cultural expec-tations to themselves (self-concepts). For converging data withyoung children see Cvencek et al. (2011), and for older childrenand adolescents, see Eccles (1987), Evans, Copping, Rowley, andKurtz-Costes (2011), and Marsh (1986). However, this is not asettled issue in the literature, because the appropriate fine-grainedexperiments have not yet been done. This order of emergence andmechanisms by which stereotypes may interact with self-conceptsis an empirical question deserving of more study.

Fourth, these findings extend prior results. Whereas del Río andStrasser (2013) assessed Chilean kindergarteners’ explicit stereo-types about mathematics, the current study assessed both implicitand explicit stereotypes, and kindergarteners’ implicit and explicitmath self-concepts. Using this combination of measures, we foundthat boys demonstrated a gender stereotype (math � boys) onimplicit measures (see Figure 1). A similar pattern of effects wasalso obtained with the implicit math self-concept measures (seeFigure 2). The finding that 5-year-old children are demonstratinggender differences on implicit but not on explicit measures of bothstereotypes and self-concepts is interesting developmentally. Chil-dren seem to first register stereotypes via their implicit cognitivesystems even when they are not able to introspect and explicitlyverbalize their stereotyped inklings. Implicit measures may capture

Figure 5. Conceptual model of explicit math self-concept for girls and boys and standardized coefficients forthe final (unconstrained) model. Standardized coefficients for girls are outside the parentheses; standardizedcoefficients for boys are inside the parentheses. � p � .05. �� p � .01.

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11KINDERGARTENERS’ BELIEFS ABOUT MATHEMATICS

nascent representations that do not rise to the level of consciousawareness, which can be assessed through Likert-scales and self-report measures. The current results add to the growing literatureshowing that implicit measures are a useful tool for investigatingyoung children’s beliefs and attitudes that children may havedifficulty expressing in words (e.g., Cvencek, Fryberg, Covarru-bias, & Meltzoff, 2018; Dunham, Baron, & Banaji, 2016).

Parents’ Math–Gender Stereotypes and MathSelf-Concepts

Chilean parents demonstrated both implicit and explicit math–gender stereotypes, and both were highly significant. Post hocanalyses indicated that the strength of those parental stereotypesdid not significantly vary for parents of girls versus boys (see theonline supplemental material). This suggests that cultural stereo-types permeate minds of adults, regardless of their own personalexperience with raising a son or a daughter.

Chilean parents also demonstrated math self-concepts that werein line with those gender stereotypes: Fathers identified withmathematics and mothers did not. Although mothers demonstratedneutral self-concepts on implicit measures (i.e., equally strongassociations of me � math and me � language), they reported astrong identification with language on explicit measures. It iscommon in adult studies for the implicit and explicit measures tobe divergent (e.g., Hofmann, Gawronski, Gschwendner, Le, &Schmitt, 2005), but why would such an effect occur in this par-ticular domain? One possible explanation may be that, regardlessof their working status—only a third of the workforce in Chile isfemale—women are responsible for most of the household chores,including caretaking of children (Ministry of Labor, 2017). Be-cause caretaking duties often involve reading to children at bed-time (and perhaps not doing bedtime mathematical puzzles), moth-ers may come to identify strongly with language, and also, Chileansociety has a strong literary tradition of female writers (e.g., IsabelAllende, Gabriela Mistral), which may also contribute to Chileanfemales in explicitly identifying themselves more with languagethan with mathematics.

It is also noteworthy that, for parents, the explicit and implicitstereotypes were strongly in the same direction as one another, andthe same was true between explicit and implicit self-concepts. Forchildren, however, such evidence was weak or nonexisting. Fur-ther research may help clarify why this might be the case.

Girls’ Early Math Self-Concepts

In this sample of Chilean kindergarteners, girls’ and boys’ mathself-concepts were related to different family factors as discussedbelow.

Differential relations between mothers’ and fathers’ mathself-concepts to girls’ math self-concepts. Mothers’ math self-concepts were positively related to girls’ self-concepts, whereasfathers’ math self-concepts were negatively related to girls’ self-concepts. Children generally tend to identify with the parent oftheir own gender (Maccoby, 2003), and for girls, this would meantheir mothers. Because Chilean mothers do not identify with math-ematics, as our results show, then girls may not identify withmathematics either. One specific process by which the weak mathself-concepts may transfer from mothers to their daughters is

mothers’ less frequent use of mathematics-related language withtheir daughters than with their sons (Chang, Sandhofer, & Brown,2011). Such differential home numeracy practices for sons versusdaughters may be especially influential in children’s early devel-opment. Another possible process may derive from mothers pro-viding girls with fewer opportunities to play with mathematics-related games (Bleeker & Jacobs, 2004; see also Master, Cheryan,Moscatelli, & Meltzoff, 2017). Such parental practices might resultin mothers conveying the message—either explicitly or implicitly—to their daughters that “math girls.” Girls are highly exposed tostrong parental messages about what is appropriate to do as afemale (see Martin, 1995).

A related finding is that fathers’ math self-concepts were neg-atively associated with their kindergarten girls’ math self-concepts.This is consistent with evidence suggesting that fathers’ implicitgender stereotypes about mathematics and language predict chil-dren’s math–gender stereotypes (Galdi et al., 2014). If girls do notprimarily identify with their fathers, then they also may not iden-tify with the qualities that fathers exhibit (father � math; thereforeme math). Consequently, young girls may begin to adopt theview that mathematics is not for them, not only because theyidentify with their mother (who does not identify with mathemat-ics), but also because they do not identify with their father (whodoes identify with mathematics). This would be consistent with thetheoretical viewpoint that young children tend toward a state of“psychological balance” or cognitive consistency among theiridentities, beliefs, and attitudes (Cvencek et al., 2014, 2016).

We also found, however, that the negative association of fa-thers’ stereotypes and self-concepts with young girls may beattenuated by fathers’ mathematics-related practices: The fre-quency with which fathers do engage in home numeracy activitieswith their daughters was positively related to their daughters’ mathself-concept. One possible implication of our findings is that,despite stereotyped beliefs that fathers may hold about mathemat-ics and gender in general, their engaging in mathematics-relatedactivities with their own daughters in terms of overt behavior mayhave a beneficial effect on their daughters’ emerging math self-concepts.

We would like to underscore that the findings reported here donot necessarily represent causal relations. Alternative explanationsmay exist for the association between parents and children’s vari-ables in this study. For example, these associations may be due toa third factor. Some candidate factors could be: (a) the influence ofthe child’s teacher on the belief system of both child and parent, or(b) family specific events or experiences that have caused similarattitudes toward mathematics in both parents and their children.Moreover, children’s own behaviors and preferences could them-selves influence their parent’s views about gender and mathemat-ics or their tendency to get involved in mathematical activities withtheir child. Future work should set out to explicitly test thesealternative explanations for the associations between parents’ andchildren’s variables through experimental and quasi-experimentalstudies.

Relation between SES and girls’ math self-concepts. Thepath modeling found that girls’ math self-concepts were associateddirectly with SES, even after taking into account the parents’measures. This suggests that the effect of SES is not exhausted byparental processes and reaches children through other mechanismsas well. In Chile, TV and other media are likely candidates for

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12 DEL RÍO ET AL.

conveying messages to children about how people from differentsocial classes and gender are expected to behave. Moreover, somestudies suggest that children from lower SES are exposed torelatively larger amounts of media (Dennison, Erb, & Jenkins,2002), and thus may be more likely to receive gender stereotypesportrayed through media, influencing their developing beliefsabout who does mathematics. Another possible bridge betweenSES and the child’s math self-concept is the extended family,which is of great importance in Chile and other Latin Americancountries. Highly frequent contact with grandparents is common inChilean families, and this may multiply the impact of societalstereotypes about gender that are likely to be more pronounced bythose raised in more traditional times.

Limitations and Future Research

The current study has four limitations. First, future researchcould explore other factors not included in this study that mighthelp us better explain the sources of young children’s early devel-oping math stereotypes and math self-concepts. For example,teachers are socializing agents that may provide input about whodoes and does not do mathematics. In elementary school, it hasbeen shown that teachers’ gender stereotypes about their students’mathematical ability can lead students to endorse math–genderstereotypes themselves (Gunderson et al., 2012; Keller, 2001). Theinclusion of kindergarten teacher data, an age group that has yet tobe studied, could help further illuminate this topic.

Second, the measure of explicit stereotypes assessed stereotypesabout mathematical liking, which are conceptually distinct fromthose about underlying mathematical ability (Master, Cheryan,Moscatelli, et al., 2017). For example, stereotype threat is triggeredin young children by the stereotypes about ability and not by theliking stereotypes (Galdi et al., 2014). How early children acquirestereotypes about mathematical ability is an important avenue forfuture work (see Bian et al.’s, 2017, related work on the acquisitionof gendered beliefs about “brilliance”). A related issue is that themeasure of explicit stereotypes used here did not offer children“both” as a choice for their answer. Note, however, that themeasures used are statistically capable of revealing no stereotyping(i.e., a score of, or close to, zero). Other explicit measures ofgender stereotyping in children (e.g., Liben & Bigler, 2002), whichallow for “both” responding, may be useful in future investiga-tions.

Third, in our attempt to make explicit measures directly com-parable to IAT measures and parental measures directly compara-ble to the child measures, we (a) relied heavily on the use of one-and two-item measures, and (b) assessed math–gender stereotypessolely in relation to reading–gender stereotypes. Nevertheless, it isworth noting that two-item measures often exhibit similar orhigher internal consistency (s � .75) as multidimensional mathself-concept measures that are based on six items when used withchildren (Marsh et al., 2002). In addition, reading is a naturalcontrast to mathematics because (a) reading and mathematicseducation are mandated from the first grade onward and (b)standardized tests across many countries have reading and math-ematics portions. Future studies will profit from measuring mathstereotypes and math self-concepts as multidimensional constructs(Marsh et al., 2002).

Fourth, the present study is based on correlational data. Analternative explanation of the direction of effects reported herecould be that girls who are good at mathematics—and who believethat mathematics is “for them”—may elicit different numeracypractices from their parents. We made a concerted effort to testseveral alternative models in our path analyses but recognize thatthese analyses do not provide clear causal direction. Theoreticalmodels that place the analytic emphasis on the interdependenteffects of the child and environment (e.g., family, school, andcultural agents) to examine the bidirectional relations will beuseful in documenting transactional processes in children’s cogni-tive and social-emotional development (Bronfenbrenner, 1979;Sameroff, 2010). It would also be useful for further studies to beconducted in a longitudinal manner, which would allow us to tracesocietal, family, and gender issues in the same children over time.We found that the math–gender stereotypes of the preschoolchildren do not (yet) match the very strongly stereotyped views oftheir parents (see Figure 1). Further developmental and longitudi-nal work, using both implicit and explicit measures over time, willbe labor intensive, but of great interest, based on the groundworklaid here.

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Received July 19, 2017Revision received August 28, 2018

Accepted October 8, 2018 �

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16 DEL RÍO ET AL.